Indonesian Journal of Forestry Research Vol. 11 No. 2, October 2024, 279-298

ISSN 2355-7079/E-ISSN 2406-8195

GOLDEN RATIO INTERPRETATION ON 150 FLOWERS:
THE BASIC INFORMATION TO DEVELOP ECOTOURISM
IN BOGOR, INDONESIA
Muhammad Moldynniz Mutiara*, Ricky Avenzora, and Harnios Arief
Department of Tropical Biodiversity Conservation, Bogor Agricultural University,
Jl. Ulin, IPB Dramaga Campus, Dramaga Bogor, West Java, 16680, Indonesia

1

Received: 18 June 2023, Revised: 11 January 2024, Accepted: 24 october 2024
GOLDEN RATIO INTERPRETATION ON 150 FLOWERS: THE BASIC INFORMATION TO
DEVELOP ECOTOURISM IN BOGOR, INDONESIA. The Aesthetic value is one of the factors in
order to attract tourists to visit. Flowers are one form of tourist attraction that symbolizes beauty, flowers
can be used as an object of interpretation for the development of ecotourism, especially in interpreting the
meaning of the aesthetic value. Assessment of beauty can be measured by a number that is believed to have
beauty, namely by using the golden ratio. Research has shown that the golden ratio actually exists in flowers.
The knowledge of the golden ratio of flowers, in addition to increasing tourist attraction, can also be used
as an interpretation for tourists because the aesthetic value is very important to the human relationship with
nature, and the motivation to protect it. Golden ratio analysis was performed on 150 flowers. A flower is
said to have a golden ratio if the ratio results in a comparison of flower morphology producing a number
of 1.618 or close to that number. The discovery of the golden ratio in all flowers shows that flowers are
creations that have aesthetic value so visitors are expected to be able to interpret the importance of the value
of beauty in living things for their tour experience.
Keywords: Aesthetic value, ecotourism interpretation, flower, golden ratio
INTERPRETASI RASIO EMAS PADA 150 BUNGA: INFORMASI DASAR UNTUK
MENGEMBANGKAN EKOWISATA DI BOGOR, INDONESIA. Nilai estetika merupakan salah satu
faktor untuk menarik minat wisatawan untuk berkunjung. Bunga merupakan salah satu bentuk daya tarik wisata yang
melambangkan keindahan, bunga dapat dijadikan objek interpretasi untuk pengembangan ekowisata, khususnya dalam
memaknai nilai estetika. Penilaian kecantikan dapat diukur dengan angka yang diyakini memiliki nilai keindahan yaitu
dengan menggunakan rasio emas. Penelitian telah menunjukkan bahwa rasio emas benar-benar ada pada bunga. Pengetahuan
rasio emas bunga selain untuk meningkatkan daya tarik wisata juga dapat dijadikan sebagai interpretasi bagi wisatawan
karena nilai estetika sangat penting bagi hubungan manusia dengan alam, serta motivasi untuk menjaganya. Analisis rasio
emas dilakukan pada 150 bunga. Suatu bunga dikatakan memiliki rasio emas jika rasio hasil perbandingan morfologi bunga
menghasilkan angka 1,618 atau mendekati angka tersebut. Ditemukannya rasio emas pada semua bunga menunjukkan
bahwa bunga merupakan ciptaan yang memiliki nilai estetika, sehingga pengunjung diharapkan mampu memaknai pentingnya
nilai keindahan pada makhluk hidup untuk pengalaman berwisata mereka.
Kata kunci: Bunga, interpretasi ekowisata, nilai estetika, rasio emas

*

Corresponding author: dynnizo@gmail.com

©2024 IJFR. Open access under CC BY-NC-SA license. doi:10.59465/ijfr.2024.11.2.279-298

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Indonesian Journal of Forestry Research Vol. 11 No. 2, October 2024, 279-298

I. INTRODUCTION
The Aesthetic value is one of the factors in
order to attract tourists to visit. Aesthetic values
in the field of tourism cannot be separated
from one another. In terms of aesthetic
connotations, tourism aesthetics mainly refers
to tourists' personal experiences, appreciation
and creation of beauty in the travel process (Li,
2017). Aesthetic value is what people “feel”
about a particular landscape, and aesthetic
value can influence tourists' perceptions of a
destination and their sightseeing experience to
other parts of the trip and then to other parts of
the destination (Wang et al., 2008). Flowers are
one form of tourist attraction that symbolizes
beauty (Chan, 2015), or jewelry (Hůla &
Flegr, 2016). Flowers have become something
interesting to study, both by definition (Nadot
& Dodinet 2016), studying the morphology of
various flower species (Hamim et al., 2019) to
their benefits for various purposes of human
life (Chen et al., 2020; Jauker et al., 2012). Based
on these matters, flowers can be used as an
object of interpretation for the development
of ecotourism, especially in interpreting the
meaning of the aesthetic value.
Assessment of beauty can be measured
by a number that is believed to have beauty,
namely by using the golden ratio (Iosa, 2018).
This ratio is believed to be the divine ratio or
golden number (Kissinger, 2012; Sharif, 2014).
The golden ratio is the ratio between the parts
or dimensions of one element. In other words,
for a line, the ratio must fall between the two
halves. The result of this ratio is 1.618 (Baiz &
Khoshnaw, 2017; Ching, 2014). Based on the
etymology of the word symmetry, as well as
on specific examples and theories of beauty,
golden ratio can also characterize symmetrical
forms (Prokopakis et al., 2013). This ratio has
been widely used in the fields of architecture
(Agustin & Utomo, 2018; Ali & Prasetia, 2021;
Astrini et al., 2015), art (Omotehinwa, 2013;
Thapa & Thapa, 2018; Yulius, 2018), even in
the forestry sector (Zelić, 2006).

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Research has shown that the golden ratio
actually exists in flowers. When observing
sunflower seeds, a rotation will be produced
which contains Fibonacci numbers (Naylor,
2002). Furthermore, many flowers have petal
arrangements that correspond to Fibonacci
numbers. Some have single or multiple lobes.
Three petals are more common, as in lilies and
irises. Some have 5 petals, such as buttercup,
wild rose, larkspur, and columbine. Some have
8, 13, 21, 34, 55 or even 89 petals. All of these
numbers are sequential Fibonacci numbers
(Akhtaruzzaman & Shafie, 2011; Koshy, 2018;
Omotehinwa, 2013).
The knowledge of the golden ratio of flowers,
in addition to increasing tourist attraction, can
also be used as an interpretation for tourist
areas as well as interesting teaching materials
for tourists and flower lovers in Indonesia. It
is also important that the aesthetic experience
of biodiversity is the act of appreciating and
experiencing beauty through observing a
species, assemblage of species or ecosystem.
The aesthetic experience is of course very
important to the human relationship with
nature, and the motivation to protect it (Langlois
et al., 2022; Tribot et al., 2019).
II. MATERIAL AND METHODS
This research was conducted in Bogor City,
Bogor Regency to include Cianjur Regency with
records that tend to be close to the Bogor area.
The specific research locations are the Bogor
Botanical Gardens, Cibodas Botanical Gardens,
Research Center for Medicinal and Aromatic
Plants (Balittro), Ornamental Plant Research
Center (Balithi), Taman Bunga Nusantara, and
locations such as roads and yards where there
are flowers. The criteria for choosing a location
are a location that has quite a large collection
of flowers based on the initial survey data.
The choice of sites increased as the research
progressed until a total of 150 flowers could be
filled.

Golden Ratio Interpretation On 150 Flowers ...................................(Muhammad M. Mutiara et al.)

A. Methods
The research data collected includeds
primary and secondary data. The primary data
in this study was the use of the golden ratio
in flowers obtained through the documentation
on the front view or/and side view of the
flower surface. These data were obtained from
the research locations. Secondary data in this
study included flower taxonomy as material
for categorizing flowers into families of each
flower. The data were obtained from the
plant encyclopedia. Special applications for
identifying plants were used when collecting
data.

The method used was field observation
by observing, measuring, and documenting
flowers in the case study areas. Data obtained
through field observations, namely the size
of the flower including the size of the petals,
crown, stalk, and overall height of the flower.
The tool used to obtain flower sizes was a
caliper, while images of flowers were obtained
using a camera.
There were 150 flowers to be selected in this
study. The list of flowers was categorized by
the family of the flower (Table 1).

Figure 1. Research location

Table 1. List of 150 flowers based on their family
No.

Family
Acanthaceae

Species
Bengal clockvine (Thunbergia grandiflora)*, Chinese violet (Asystasia gangetica),
firecracker flower (Crossandra infundibuliformis), golden shrimp plant (Pachystachys lutea)*,
green chiretta (Andrographis paniculata), Mexican petunia (Ruellia simplex), Mexican
shrimp plant (Justicia brandegeeana), mysore trumpetvine (Thunbergia mysorensis),
Philippine violet (Barleria cristata), yellow-vein eranthemum (Pseuderanthemum
maculatum)

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Table 1. Continued
No.

Family
Agavaceae
Alismataceae
Amaranthaceae
Amaryllidaceae
Annonaceae
Apocynaceae

Araceae
Asteraceae

Balsaminaceae
Begoniaceae
Bignoniaceae
Caesalpiniaceae
Campanulaceae
Cannaceae
Caricaeae
Commelinaceae
Convolvulaceae
Costaceae
Cucurbitaceae
Dilleniaceae
Ericaceae
Euphorbiaceae
Fabaceae
Gesneriaceae
Iridaceae
Lamiaceae

Liliaceae
Linderniaceae
Lythraceae

282

Species
Tuberose flower (Polianthes tuberosa)*
Water jasmine (Echinodorus palaefolius)
Cockscomb flower (Celosia argentea), globe amaranth (Gomphrena globosa)*
African lily (Agapanthus praecox), Amazon lily (Eucharis amazonica)*, beach spider lily
(Hymenocallis littoralis), Eucrosia bicolor, striped barbados lily (Hippeastrum striatum), white
rain lily (Zephyranthes candida)
Ylang-ylang (Cananga odorata)*
Frangipani flower (Plumeria rubra), kopsia (Kopsia arborea), Madagascar periwinkle
(Catharanthus roseus), pinwheel flower (Tabernaemontana divaricata), purple allamanda
(Allamanda blanchetii), sea mango (Cerbera manghas)*, yellow allamanda (Allamanda
cathartica)
Flamingo flower (Anthurium andraeanum), peace lily (Spathiphyllum wallisii)
Barberton daisy (Gerbera jamesonii), cobblers pegs (Bidens pilosa), dahlia (Dahlia
pinnata), elegant zinnia (Zinnia elegans), gold medallion (Melampodium divaricatum),
Indian chrysanthemum (Chrysanthemum indicum), king’s salad (Cosmos caudatus)*,
marigold (Tagetes erecta), Mexican fleabane (Erigeron karvinskianus), Mexican tournesol
(Tithonia diversifolia)*, wedelia (Sphagneticola trilobata)*
Bussy lizzy (Impatiens walleriana)*, garden balsam (Impatiens balsamina)*, New Guinea
impatiens (Impatiens hawkeri)*
Polka dot begonia (Begonia maculata), wax begonia (Begonia cucullata)
African tulip tree (Spathodea campanulata)*, rosy trumpet tree (Tabebuia rosea)*, yellow
trumpet bush (Tecoma stans)*
Candle bush (Senna alata)*
Star of bethlehem (Hippobroma longiflora)
African arrowroot (Canna indica)
Papaya (Carica papaya)
Murdannia nudiflora, oyster plant (Tradescantia spathacea)
Cairo morning glory (Ipomoea cairina)*, morning glory (Ipomoea indica)*, sweet potato
(Ipomoea batatas), water spinach (Ipomoea aquatica)
Crepe ginger (Costus speciosus)*
Cucumber (Cucumis sativus)
Elephant apple (Dillenia philippinensis)*
Azalea (Rhododendron indicum), Flame Azalea (Rhododendron calendulaceum)
Coral plant (Jatropha multifida), crown of thorns (Euphorbia milii)*, gout plant (Jatropha
podagrica), Peregrina (Jatropha integerrima),
Asian pigeonwings (Clitoria ternatea)*, butterfly tree (Bauhinia purpurea)*, Calliandra
surinamensis*, jade vine (Strongylodon macrobotrys), pinto peanut (Arachis pintoi), peacock
flower (Caesalpinia pulcherrima), vegetable hummingbird (Sesbania grandiflora)*
Copper leaf (Chrysothemis pulchella), Seemannia sylvatica
African iris (Dietes bicolor), blue star (Aristea ecklonii), montbretia (Crocosmia
crocosmiiflora), walking iris (Trimezia longifolia), water iris (Neomarica gracilis)
Bleeding glory-bower (Clerodendrum thomsoniae)*, cat's whiskers (Orthosiphon aristatus)*,
Chinese hat plant (Holmskioldia sanguinea), great basil (Ocimum basilicum), Coleus (Coleus
scutellarioides), Lavender (Lavandula angustifolia), Mealy Sage (Salvia farinacea), scarlet
sage (Salvia splendens), white teak (Gmelina arborea)*
Yellow daylily (Hemerocallis lilioasphodelus)
Wishbone flower (Torenia fournieri)
Taiwan beauty (Cuphea hyssopifolia), Thai crape myrtle (Lagerstroemia floribunda)*

Golden Ratio Interpretation On 150 Flowers ...................................(Muhammad M. Mutiara et al.)

Table 1. Continued
No.

Family
Magnoliaceae
Malvaceae
Melastomataceae
Nyctaginaceae
Nymphaeaceae
Ochnaceae
Oleoaceae
Orchidaceae

Oxalidaceae
Passifloraceae
Plumbaginaceae
Polygonaceae
Pontederiaceae
Punicaceae
Rosaceae
Rubiaceae
Rutaceae
Saururaceae
Scrophulariaceae
Solanaceae
Talinaceae
Verbanaceae
Zingiberaceae

Species
White champaca (Magnolia alba)*
Caesar weed (Urena lobata), Chinese hibiscus (Hibiscus rosa sinensis), Chinese-lantern
(Abutilon pictum), guest tree (Kleinhovia hospita), sleeping hibiscus (Malvaviscus arboreus)
Heterocentron subtriplinervium, Malabar melastoma (Melastoma malabathricum), princess
flower (Tibouchina urvilleana)
Great bougainvillea (Bougainvillea spectabilis)*
Lotus (Nymphaea lotus), Nymphaea nouchali var careulea,
Mickey mouse flower (Ochna serrulata)
Common jasmine (Jasminum officinale), jasmine (Jasminum sambac), night blooming
jasmine (Nyctanthes arbor-tristis)*
Boat orchid (Cymbidium sinense), hooded orchid (Dendrobium aphyllum), moon orchid
(Phalaenopsis amabilis)*, oncidium sharry baby, Philippine ground orchid (Spathoglottis
plicata)*, scorpion orchid (Arachnis flos-aeris), spider orchid (Brassia sp.), venus slipper
(Paphiopedilum acmodontum)
Bilimbi (Averrhoa bilimbi)
Ramgoat dashalong (Turnera ulmifolia)
Ceylon leadwort (Plumbago zeylanica)*
Coral vine (Antigonon leptopus)*
Pickerelweed (Pontederia cordata)
Pomegranate (Punica granatum)
Red rose (Rosa kordesii), white rose (Rosa alba)
Ashanti blood (Mussaenda erythrophylla), cape jasmine (Gardenia jasminoides)*, Egyptian
starcluster (Pentas lanceolata), Indian mulberry (Morinda citrifolia)*, Pavetta indica, West
Indian jasmine (Ixora javanica)
Orange jasmine (Murraya paniculata)*
Fish leaf (Houttuynia cordata)*
Fountain bush (Russelia equisetiformis)*
Brazil's white angel trumpet (Brugmansia suaveolens)*, Brunfelsia uniflora*, chili (Capsicum
frutescens), petunia (Petunia atkinsiana), potato (Solanum tuberosum)
Fame Flower (Talinum paniculatum)
Blue fountain bush (Clerodendrum serratum), blue porterweed (Stachytarpheta jamaicensis),
Clerodendrum calamitosum, common lantana (Lantana camara), golden dewdrop (Duranta
erecta), purple wreath (Petrea volubilis)
Aromatic ginger (Kaempferia galanga), shell ginger (Alpinia zerumbet), tumeric (Curcuma
domestica)

Note: *) Flowers from the forest

B. Analysis
The data that has been obtained was
described digitally to facilitate the analysis of
the proportion of the golden ratio. Calculation
of the golden ratio was done by first looking at
the morphology of each flower. Analysis can be
done by comparing the length of the flower to
the stem, and the overall size of the flower. The

documentation results that have been obtained
from the object were then compared with the
golden ratio formula (See Figure 2).
Flowers that are considered to contain the
golden ratio, that is, if the height, length, width,
and area of the object are divided then produce
numbers, namely 1.618 or close to that number.
If there is a ratio that has a number very far

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Figure 2. An example of calculating the golden ratio in flowers

from 1.618, then the flower does not contain
the golden ratio in it. A number is said to be
the golden ratio if the ratio of numbers (for
example a+b) divided by a larger number (b)
is the same as the result of the large number
divided by a smaller number (b/a) (Benjafield
& Davis, 1978; Green, 1995). If the numbers
obtained are far from the numbers 1.618
and 0.618, then it can be said that the flower
that has been measured does not contain the
golden ratio. The applications used in this
study are Adobe Photoshop and Image J. The
measurement results are then processed using
the Adobe Photoshop application with a line
forming tool used to make comparison lines
to obtain the existence of the golden ratio in
the flower that has been measured. The ImageJ
application is used to get results in the form of
area comparisons. The golden ratio has a close
relationship with Fibonacci numbers (Fn = Fn1+Fn-2) (Chasnov, 2016; Livio, 2002), so one
example of the ratio in the area can be found
in the total area of a flower (the majority of 5
petals) with an area of 3 petals.
III. RESULT AND DISCUSSION
1. Golden Ratio on Flower
Based on the table list of flowers (Table 1), the
family with the most flowers in this study is the
Asteraceae family, totaling 11 species. Followed
by the Acanthaceae and Lamiaceae families
with 9 species, Orchidaceae with 8 species, and
so on. The analysis revealed that most flowers
exhibit the golden ratio or values ​​that closely

284

match it.. The difference in the values on the
flowers has various factors. Mainly, flowers
that have a larger size will get a golden ratio of
1.618 compared to smaller flowers. Further, the
golden ratio number (1.618) has three decimal
places, while the research measurement tool
only produced one decimal point. Weaknesses
in the tool made the obtained value only close
to 1.618. There were flowers that contain one
golden ratio, two golden ratios, three golden
ratios, and four golden ratios. For example, the
moon orchid contains two golden ratios, the
first ratio between the total width of petals with
the width of one petal, the second ratio between
the total height and the height of the labellum
(See Figure 2). The following is a graph of the
number of golden ratios of the studied flowers.
The findings showed that 66.7% or 100
flowers contain 2 golden ratios in them. There
were variations in the golden ratios of the
flowers, however, each flower was noted to have
golden ratio in the ratio of area and the ratio of
distance. The distance ratio, which is the ratio
between the total length and the length of the
crown, is also the ratio of the length and width
of the flower. Flowers with three golden ratios
were also noticed, with a proportion of 22.7%
or 34 flowers. Flowers with only one golden
ratio were found with a proportion of 8.7%.
Moreover, only one flower (wishbone flower)
or 0.7% was noted with four golden ratios with
a proportion of 0.7%.
The golden ratio are influenced by various
flower morphologies, therefore the obtained
results were vary. The analysis found 12

Golden Ratio Interpretation On 150 Flowers ...................................(Muhammad M. Mutiara et al.)

Figure 3. Total golden ratio based on findings on flower

Figure 4. Type of golden ratio on flower

comparisons of the golden ratio in the flowers.
The golden ratio that most flowers have is the
ratio of area (type 1). Type 2 is the golden ratio
between the length and width of the flower,
type 3 is the ratio of the total height of the
flower to the height of the crown to the stalk or
other parts, type 4 is the ratio of the diameter/
length/width of the total flower to the length/
height of the crown of one flower, type 5 is the
ratio of the length to the tube with the length
of one flower petal, type 6 is the ratio of the
part of the flower that has a split, type 7 is
the ratio of the long and short distances, type
8 is the ratio of the flower pattern, type 9 is
the ratio of the height and width of the flower,

type 10 is the ratio of the slanted side and the
base, type 11 is the ratio of the circumference,
and finally type 12 is the ratio of 2 petals with
different size. The following is a graph of the
comparison of the golden ratios found in this
study and the amount of flowers from each
type (see Figure 4). The list of flowers classified
based on the type of golden ratio found is
presented in Table 2.
Area comparison was the result of the golden
ratio that was most often found in this study.
The results of the analysis using the ImageJ
application showed that a comparison of the
total area with the area of various parts of the
flower can produce the golden ratio number

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Table 2. List of flowers by type of the golden ratio
No.

286

Type of golden
ratio

Species

Interpretation message for visitors

The ratio of area

133 flowers except for the african tulip
tree, barberton daisy, bussy lizzy, Calliandra
surinamensis, crown of thorns, flamingo
flower, lavender, lotus, marigold, mealy sage,
mickey mouse flower, mysore trumpetvine,
Nymphaea nouchali var. caerulea, pinto peanut,
shell ginger, turmeric, West Indian jasmine

Findings on area comparisons are generally
found in the comparison between the total flower
crown strands (5 strands) versus 3 flower crown
strands. This shows that there are Fibonacci
numbers in flowers. The number of strands in
each flower gives a flower a beautiful value

The ratio between
the length and
width of the flower

African arrowroot, African tulip tree,
aromatic ginger, azalea, bleeding glory-bower,
blue fountain bush, blue porterweed, cape
jasmine, Chinese hibiscus, Chinese violet,
Clerodendrum calamitosum, cobblers pegs, coral
vine, crepe ginger, Egyptian starcluster,
fame flower, flame azalea, flamingo flower,
frangipani flower, green chiretta, gout plant,
jasmine, king’s salad,, Malabar melastoma,
Murdannia nudiflora, peace lily, peregrina,
Philippines ground orchid, pinwheel flower,
princess flower, purple wreath, ramgoat
dashalong, scorpion orchid, sea mango,
Seemannia sylvatica, striped barbados lily, Thai
crape myrtle, venus slipper, walking iris, West
Indian jasmine, white rain lily, yellow-vein
eranthemum, yellow trumpet bush

The comparison of flower length and width in
this finding can be in the form of the total flower
size or flower parts such as flower petals. This
finding shows that the length and width of some
flower species are proportional. This balanced
part creates aesthetic value.

The ratio of the
total height of the
flower to the height
of the petals to the
stalk or other parts

Candle bush, cat’s whiskers, cockscomb
flower,
Eucrosia
bicolor,
Heterocentron
subtriplinervium, golden shrimp plant, guest
tree, lavender, Mexican shrimp plant, moon
orchid, Mysore trumpetvine, pinto peanut,
peacock flower, shell ginger, scarlet sage,
sleeping hibscus, tuberose flower

The golden ratio in the ratio of flower height
shows that the flower grows while showing its
beauty value.

The ratio between
total length and
one petal

Abutilon pictum, African lily, Amazon lily,
aromatic ginger, ashanti blood, Bengal
clockvine, bleeding glory-bower, blue
fountain bush, blue star, Brunfelsia uniflora,
bussy lizzy, caesar weed, Cairo morning
glory, cape jasmine, chili, common lantana,
coral plant, crepe ginger, crown of thorns,
cucumber, dahlia, elephant apple, flame
azalea, fountain bush, golden dewdrop, globe
amaranth, great bougainvillea, guest tree,
Heterocentron subtriplinervium, Houttuynia cordata,
Indian murberry, king’s salad, lotus, marigold,
mealy sage, Mexican petunia, mickey mouse
flower, moon orchid, morning glory, New
Guinea impatiens, night blooming jasmine,
oncidium sharry baby, orange jasmine,
papaya, petunia, pickerelweed, Philippine
violet, purple wreath, red rose, rosy trumpet
tree, taiwan beauty, tuberose flower, water
jasmine, wax begonia, white champaca, white
rose, white teak, wishbone

This finding shows that the size of each part of
the flower, such as the petals, has a length that
makes the flower look beautiful. If the flower
part is longer or shorter it may not make the
flower look beautiful.

Golden Ratio Interpretation On 150 Flowers ...................................(Muhammad M. Mutiara et al.)

No.

Type of golden
ratio

Species

Interpretation message for visitors

The ratio between
the length of the
tube with the
length of one
flower petal

Barberton daisy, blue porterweed, Brazil’s
white trumpet angel, cobblers pegs,
elegant zinnia, gold medallion, Indian
chrysanthemum, Mexican fleabane, Mexican
tournesol, pomegrante, potato, purple
allamanda, sweet potato, wedelia, yellow
allamanda

This comparison is generally found in the
Asteraceae family, but there are several from
other families. The part called the tube is the
discus, which is the part of the flower that
consists of small flowers that contain nectar
which is useful for insects. These findings show
that the tube/circle-shaped part, apart from
providing aesthetic value, also provides benefits,
especially for insects.

The ratio of the
part of the flower
that has a split

Bussy lizzy, garden balsam, New Guinea
impatiens

This finding shows the uniqueness of the
Balsaminaceae family. The heart shape found on
the flower petals is the beauty value of this family.

The ratio of the
long and short
distances

Ceylon leadwort, cymbidium orchid, star of
bethlehem, water spinach

Flowers can look beautiful because they have a
proportional distance between the flower parts.
In this case, that is the distance between the two
upper flower crowns and the distance between
the lower flower crowns.

The ratio of the
flowers pattern

Aromatic ginger, Asian pigeonwings, beach
spider lily, bilimbi, Calliandra surinamensis,
coleus, copper leaf, Dietes bicolor, great basil,
montbretia, Pavetta indica, pickerelweed,
striped barbados lily, water iris, wishbone

The patterns on the flowers really give beauty to
each flower. However, if the pattern placement
is not as it currently appears, it could result in
something that is not beautiful. The finding of
the golden ratio in the patterns shows that the
patterns in the flowers are placed in a position
that can provide aesthetic value.

The ratio of the
height and width

Abutilon pictum, Houttuynia cordata, Nymphaea
nouchali var careulea, polka dot begonia,
vegetable hummingbird

The beauty of flowers can be found in various
dimensions. This finding shows that the species
in this discovery have a point of beauty when
viewed in this dimension.

The ratio of the
slanted side and the
base

Common jasmine, kopsia, Pavetta indica

The flower species in this discovery have smaller
flower petals compared to other species. The
ratio of the slanted side and the base is a finding
that shows that each petal has a growth that
contains beauty because the petals expand in the
right direction, making the flower pleasing to the
eye.

The ratio of the
circumference

Lavender, Mysore trumpetvine

This finding shows that the outer part of the
flower surrounds the inner part of the flower,
creating beautiful proportions in these two
species.

The ratio of the
2 petals with
different sizes

Butterfly flower, jade vine, lotus, Philippine
ground orchid, turmeric, yellow daylily

These findings suggest that different sizes can
provide aesthetic value. The beauty of flowers is
not only found in flowers that have similar sizes,
but different sizes can also provide beauty value.

for all the studied flowers. There were 133
flower counts showed the golden ratio in area
comparison. Generally, the area comparison
can be found in flowers that have 5 petals
than in 3 petals flowers (See Figure 5). The
results of this comparison show that there is a
relationship between the golden ratio and the
Fibonacci numbers because 3 and 5 are part of
the Fibonacci numbers. To further strengthen

the relationship between the two, this fact was
also found in flowers with 8 petals like white
jasmine and flowers with 13 strands like wedelia
flowers (see Figure 6).
The two flowers jasmine flower has 5
flower petals and wedelia flower has 8 flower
petals. The numbers 5, 8, and 13 are part of
the Fibonacci numbers, so these findings show
that there is a very close relationship between

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the golden ratio and the Fibonacci numbers
as shown in the ratio of flower area (Banerjee
& Sinha, 2019). Although many golden ratios
were found in area ratios related to Fibonacci
numbers, however, flowers with six petals and
various strand numbers may exhibit area ratios

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that align with the golden ratio. For example,
yellow-vein eranthemum, ylang, and flowers
from the Amaryllidaceae family are examples
of flowers with 4, 9, and 6 petals, that had the
golden ratio in the area ratio of these flowers
(Figure 7).

Figure 5. The golden ratio on the flower area of the Convolvulaceae family. (a) sweet potato,
(b) water spinach, (c) morning glory, and (d) Cairo morning glory

Figure 6. The golden ratio on the flowers area of (a) jasmine and (b) wedelia flower

Figure 7. The golden ratio on flowers with non-Fibonacci number of petals (a) ylang-ylang, (b) yellowvein eranthemum, (c) beach spider lily, and (d) striped barbados lily

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Golden Ratio Interpretation On 150 Flowers ...................................(Muhammad M. Mutiara et al.)

The golden ratio in the ratio between the
length and width of flowers was found in 38
flowers, which was the third highest golden
ratio found in this study. The flowers with the
golden ratio in the ratio of length to width were
frangipani flower, pinwheel flower, princess
flower, and Israel grass flowers (see Figure 8).
Ratios of the length and width of the flower
can be found in the petals and the whole flower
as in the Israel grass flower. The length of the
flower petals is the length of the flower pistil.
The Frangipani flower has a size of 26.1 mm
/16.2 mm, so the number 1.611 is obtained.
The pinwhell flower has a size of 18.2 mm /
11.3 mm then the number 1.610 is obtained.
Princess flower has a larger size than the
previous two flowers with a size of 32.8 mm

a

b

/ 20.3 mm and the number 1.615 is obtained
from this comparison. Chinese violet flower has
a small size with a size of 20.7 mm / 12.8 mm,
the number 1.617 is obtained from the ratio of
the total length and width of the flower.
The ratio of the total height of the flower
with the height of the crown to the stalk or
other parts was found in the flowers of the
cockscomb, golden shrimp plant, Mexican
shrimp, and candle bush. Other parts can be
interpreted as when the stem, flower petals, or
leaves appear (see Figure 9).
Cockscomb has a total height of 412.4
mm and a height of 254.9 mm until the leaves
appear. The results of the comparison produce
the number 1.618. Golden shrimp flower has a
total height of 103.9 mm and a height of 64.2

c

d

Figure 8. The golden ratio on (a) frangipani flower, (b) pinwhell flower, (c) princess flower, and (d) Israel
grass flower

Figure 9. Golden ratio on height. (a) cockscomb, (b) golden shrimp plant, (c) Mexican shrimp, and (d)
candle bush

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a

b

c

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d

Figure 10. The golden ratio between total length and one petal. (a) Papaya, (b) Indian mulberry, (c)
Indian blooming jasmine, (d) lotus

a

b

c

d

Figure 11. The golden ratio between the length of the tube and the length of one petal. (a) Elegant
zinnia, (b) Mexican tournesol, (c) yellow allamanda, (d) Brazil’s white angel trumpet

mm when the yellow leaves emerge, giving a
golden ratio of 1.618. As for the comparison
of the total height of 2 leaves with 1 leaf with
a size of 36.8 mm/22.7 mm, the number is
1.621. In the Mexican shrimp flower, the yield
ratio is similar to that of the wax flower, but the
flower crown is in the middle, which is different
from the wax flower, which is at the top. The
comparison of these heights is 54.2 mm/33.5
mm and 51.6 mm/31.9 mm, respectively, thus
the golden ratio is 1.618. Candle bush has a
height at the top of 80.9 mm which compares
to the height of the candle-shaped section of
50 mm. The number 1.618 was obtained in this
comparison. The results for the four flowers
show the number 1.618 because they have a large
size which makes the comparison numbers even
bigger. The larger the size obtained, the easier it
will be to obtain the golden ratio number when
compared to smaller flowers.
The ratio of total flower diameter/length/
width to the length/height of one petal is
the second highest golden ratio found in this
study. This measurement is put into a different

290

category from the ratio of the total height of
the flower because in this comparison the size
of the flower is taken from the top view of
the flower. Examples of this comparison can
be found in the previous flowers, namely the
morning glory flower and the kates sweet potato
flower. Other examples of this comparison can
be found in the papaya flower, Indian mulberry
flower, night blooming jasmine, and lotus.
The ratio of diameters can be seen in Figure
5. namely morning glory and sweet potato.
Furthermore, the ratio of the total length to
the length of one flower corolla was found
in papaya, Indian mulberry, night blooming
jasmine, and lotus flowers. The papaya flower
has a golden ratio of 19.3 mm / 11.9 mm,
which is 1.621. Indian mullbery flowers have
a total length of 9.7 mm and the length of
one crown is 6, thus the golden ratio is 1.616.
The night blooming jasmine flower has a total
length of 24 and the length of a crown of 24.5
mm thus the ratio value is quite far from the
golden ratio’s. The difference with the previous
type is in this ratio, the length of one strand is

Golden Ratio Interpretation On 150 Flowers ...................................(Muhammad M. Mutiara et al.)

taken. The night blooming jasmine flower has
a line of intersection between its flower petals.
If the length like the previous flower is taken
then then value of the golden ratio or close to
that of the golden ratio will not be obtained.
However, when measured up to the intersection
line, the sizes of 14.8 and 15.2 mm were used,
so when compared, numbers that are close to
the golden ratio would be obtained, namely
1.621 and 1.612. The lotus flower with a size of
55.7 mm / 34.5 mm when viewed from above
will produce a golden ratio of 1.614. In this
comparison, it can be found that the pistil is an
important component of creating the golden
ratio in flowers.
The ratio of the length to the tube with the
length of one flower crown is a comparison
that is almost the same as the ratio of the total
length to one flower crown, the difference is in
the length used. The length in this comparison
is the distance from the tip of the crown to
the end of the central part of the flower which
resembles a tube. Of course, the flowers that
fall into this category are flowers that have a

a

tube in the middle such as flowers from the
Asteraceae family, e.g. the elegant zinnia and
Mexican tournesol. Sweet potato (see Figure
5) has a golden ratio in this ratio type, besides
yellow allamanda and Brazil’s white angel
trumpet flowers.
Figure 13 shows the tube in the flower can
also be interpreted as the middle part of the
flower, which can be a small flower, stamens,
pistils, or whole tube. Elegant zinnia has yellow
flowers that resemble rings so that they form
a circle in the center of the flower (Gulton et
al., 2013). Mexican tournesol flowers have a
tube containing pistils and stamens, while the
yellow allamanda flower and Brazil’s white
angel trumpet flower have a complete tube
shape. The elegant zinnia flower has a ratio of
31.4 mm/19.4 mm, resulting in a golden ratio
of 1.618. Kipait with a size of 75 mm/46.4 mm
scored 1.616, yellow allamanda flowers with a
size of 66.9 mm/41.3 mm scored 1.619 and
Brazil’s white angel trumpet with a size of 77.2
mm/47.7 mm scored the golden ratio of 1.618.

b

c

Figure 12. The golden ratio of the Balsaminaceae family

a

b

c

Figure 13. The golden ratio on two different lengths. (a) star of bethlehem, (b) ceylon leadwort, (c)
cymbidium orchid

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The next golden ratio is the golden ratio
found in the Balsaminaceae family, namely
the ratio of the flower halves. The flower
morphology of the Balsaminaceae family has a
split that resembles a wing and consists of 5
flower petals (Yilin, 2001).
Based on the morphology of the three
flowers, Impatiens balsamina has a different
morphology from Impatiens hawkeri and
Impatiens walleriana. The results also show
that Impatiens balsamina only has one golden
ratio. Impatiens baslamina flower with a size
of 15.3 mm/9.5 mm thus has a ratio of 1.610.
Impatiens hawkeri flower has a cleavage size
of 21 mm/12.9 mm, thus the ratio is 1.627.
Impatiens walleriana flower with a slit size of
12.7 mm/7.9 mm gives a ratio of 1.607.
The ratio of the long and short distances
is the distance measured from the end of one
crown to the other end of the crown (Figure
13). There are only 4 flowers in this comparison,
namely Water Spinach (see Figure 5), star of
bethlehem, ceylon leadwort, and cymbidium
orchid.
The results of measuring the length of
the distance between the crowns of the stars
of the bethlehem flower were 31.4 mm at the
distance of the upper crown and 19.4 mm at
the distance of the lower crowns/base. The
result of the comparison is the golden ratio of
1.618. Ceylon leadwort has a distance between
the upper crowns of 26.9 mm and a distance
between the lower crowns/base of 16.6 mm,
thus the ratio is 1.620. Cymbidium flowers have
a longer distance between the lower crowns

a

b

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which is marked with CD and a shorter distance
marked as line AB (Figure 15). The length of
CD is 80.1 mm compared to 49.5 mm for the
length of AB, the golden ratio is obtained in
this comparison.
The golden ratio in comparison of shades
is a very unique finding because it shows
something of value in the layout of patterns
in flowers. Examples of flowers that have this
golden ratio besides wishbone flowers are
Asian pigeonwings, Dietes bicolor, montbretia,
and bilimbi.
Asian pigeonwings have a yellow pattern in
the center of the flower and a small ribbonlike crown at the top. The results of the first
measurement by comparing the total length
(42.6 mm) with the length of the pattern plus
the length of the ribbon (26.3 mm) get the ratio
of 1.619. When the length of the pattern (26.3
mm) is compared to the length of the ribbon
(16.2 mm), the golden ratio is 1.623. Dietes
bicolor flower has 2 golden ratios related to the
flower pattern. The first is ratio of the total
length (64.3 mm) to the length of one crown
to the pattern (39.7 mm), the obtained ratio
is 1.619. The second is the ratio of the length
to the center point (31.9 mm) with the length
from the center point to the end of the pattern
(19.7 mm) that resulted the same ratio of 1.619.
Bilimbi is included in this category because
the comparison found is similar to the flower
in Figure 10, but this flower has a pink color
near the pistil. The measurement result is 18.4
mm/11.4 mm and the resulted ratio is 1.614.
Montbretia flowers have a spotted pattern that

c

d

Figure 14. The golden ratio on the pattern of flowers. (a) Asian pigeonwings, (b) Dietes bicolor,
(c) bilimbi, (d) montbretia

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Golden Ratio Interpretation On 150 Flowers ...................................(Muhammad M. Mutiara et al.)

surrounds the flower pistil. The measurement
result is 48.8 mm/30.2 mm and the golden ratio
is 1.618.
The ratio of the height and width of the
flower is the golden ratio that is obtained when
the flower is viewed from the side. Some flowers
that have this golden ratio are Abutilon pictum,
Vegetable Hummingbird and Houttuynia cordata.
Abutilon pictum flower has a shape that
resembles a lamp, the golden ratio obtained
from the height and width ratio (54 mm/33.4
mm) produces a ratio of 1.617. The vegetable
hummingbird flower with a size of 61.9
mm/38.3 mm has a ratio of 1.616. The
Houttuynia cordata flower has a ratio of the
width of one crown (19.2 mm) to the height of
the pistil (11.9 mm) of 1.614.
Common jasmine, kopsia, and Pavetta indica
flowers have a golden ratio in the ratio of the
slanted side to the base. This comparison is
similar to the comparison of long and short
distances (see Figure 13), the difference between
these two golden ratios is that the distance taken
is the distance that produces a triangular shape.

Pavetta indica flower and common jasmine
flower have a slanted side which is the value of
the golden ratio, while in the kopsia flower, the
perpendicular part is the value of the golden
ratio. Pavetta indica flower has a slanted side
length of 19.4 mm and a crown length of 12
mm, thus the raio is 1.617. Common jasmine
has a size of 26.6 mm/16.5 mm thus the ratio
is 1.615. The kopsia flower has a size of 28.4
mm/17.5 mm, and the ratio is 1.622. The result
of the comparison of the slanted side and the
base which resembles a triangle shape is in
accordance with the statement of Livio (2002),
that the golden ratio is found in an object and
the shape of the triangle is an isosceles triangle
and a gnomon triangle.
Circumference comparison is a finding that
is not often found in other flowers. There are
only 2 flowers with the golden ratio found on
the circumference, namely lavender and Mysore
trumpetvine flowers. These flowers do not have
the golden ratio in area ratio, but the findings
show that the circumference ratio is owned by
these flowers.

b

a

c

Figure 15. The golden ratio between height and width. (a) Abutilon pictum, (b) Vegetable Hummingbird,
(c) Houttuynia cordata

a

b

c

Figure 16. The golden ratio on slanted side and base. (a) Pavetta indica, (b) common jasmine, (c) kospia

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b

a

Figure 17. The golden ratio on the perimeter of the flower. (a) Lavender, (b) Mysore trumpetvine

b

c

d

a

Figure 18. The golden ratio on the 2 different sizes of flower petals. (a) Philippine Ground Orchid, (b)
yellow daylily, (c) jade vine, (d) turmeric

Lavender flowers have a ratio of the total
circumference (61.212 mm) to the circumference
of the lighter-colored parts (38.064 mm), thus
the ratio is 1.608. Mysore trumpetvine flowers
have a total circumference of 156.885 mm and
a sac circumference of 97.283 mm, therefore
have a ratio of 1.612.
Many flowers have petals that are the same
size, but not all flowers have that morphology.
The results of the golden ratio show that there
is a size comparison between the 2 crowns.
Examples in this comparison can be found in
yellow daylily, Philippine ground orchid, jade
vine, and turmeric (see Figure 18).
The Philippine ground orchids have a width
ratio of larger crowns (A) and smaller crowns
(B). This comparison is also found in the
yellow daylily Flower, which is the width of the
flower crown. The comparison of jade vine and
turmeric flowers is found in the comparison of
the length of 2 flower crowns.

294

B. Ecotourism Interpretation of the Golden
Ratio in Flowers
Interpretation is an educational activity that
aims to uncover meanings and relationships
through the use of original objects with direct
experience (Tilden, 2007). Interpretation
activities can be carried out in ecotourism
development, one of the subjects that can
be applied is flowers. Interpretation can be
successful if the program can give visitors
something new to learn (Helianthi, 2022).
This statement is a justification for Larsen's
statement that interpretation is a guide, directing
the audience from physical resources to the
underlying meaning, from the tangible to the
intangible, and from sight to insight (Larsen,
2011). By providing opportunities to connect
with the meaning of resources, interpretations
provoke public participation in resource
management. Interpretation can help visitors to
understand their relationship and their impact

Golden Ratio Interpretation On 150 Flowers ...................................(Muhammad M. Mutiara et al.)

on the resource. The existence of interpretation
is expected to help visitors to care.
Knowledge of the golden ratio in flowers
can be the subject of an interpretation program
because this discovery is something new and can
be useful for visitors to understand the beauty
of a flower. Visitors will get the meaning that
a creation made by God is not done randomly.
This is supported by Gardiner's statement that
when looking at flowers that have a morphology
based on the golden ratio, human consciousness
will think that flowers are something beautiful
(Gardiner, 2012). Based on the perspective of
Muslims, the discovery of the golden ratio in
flowers has been implicitly explained through
the Holy Scriptures. Al-Quran in surah Al-Mulk
(67) verse 3 and surah Al-Infitar (82) verse 7
which reads as follows.
Surah Al Mulk (67) verse 3

3. “Who created the seven heavens in layers.
You will not see anything unbalanced in the
creation of a loving God. So, look once more,
do you see anything that is flawed?”
Surah Al Infitar 82 verse 7

7. “Who created you then perfected
your events and made your (body structure)
balanced”
It is explained in Tafsir Ibnu Katsir that Surah
Al-Mulk verse 3 that all of God's creations are
mutually compatible and balanced. In the next
surah, it is explained that in fact humans were
created in a balanced and very good form. The
two verses of the holy Al-Quran show that there
is nothing that is not balanced. The golden ratio
is a comparison which, in addition to containing
the value of beauty, has the meaning of balance
to create something beautiful. The discovery
of the golden ratio in flowers proves the truth
of the holy verses of the Quran and the truth
of the golden ratio theory. Surah Al Infitar 82
verse 7 has been researched that humans have

a relationship with the golden ratio (Mardhiyati
et al., 2018). The use of the holy verses of the
Al-Quran to interpret the golden ratio can be
a reference for interpreters in explaining the
golden ratio to the audience so that they can
better understand the importance of knowing
the golden ratio in flowers.
The interpretation that can be outlined
from the discovery of the golden ratio in
flowers apart from a religious perspective can
be seen in terms of the benefits of the plants
studied. Based on literacy results, 65.4% of
the flowers studied were flowers that had
medicinal benefits, 20.7% had benefits for
Indonesian culture and then they were only
useful as ornamental plants. Yellow Allamanda
flower, for example, is a medicinal plant that
can prevent complications from malaria and
swelling of the spleen (Munawaroh et al., 2017).
Star of Bethlehem as eye drops to cure cataracts
(Rahayu & Andini, 2019). Cambodian flowers
have a close relationship with Balinese culture
(Sujarwo & Lestari, 2018) as well as Jasmine and
Ylang-ylang flowers which are widely used for
ceremonies packaged in the form of 7 Kinds
of Flowers (Ciptaningrum et al., 2022; Nurhadi
et al., 2018). Knowledge of the benefits of
flowers is something that is used as interesting
material for tourists so that the ancient people
might first see the beauty contained in flowers
so that eventually they can find their benefits
as medicinal plants and for the culture of the
local community. Further, the measure of the
golden ratio of a flower can also be used to
determine the value of uniqueness in the One
Score One Criteria Scoring System (Avenzora,
2008). The system shows that every single score
given must be accompanied by the fulfillment
of one discrete indicator requirement. The
system shows that every single score given must
be accompanied and fulfill the requirements of
one discrete indicator, so the golden ratio can
be used to assess the uniqueness of that system.
Based on all the previous explanations, the
golden ratio of flowers is an interpretation of
the value of beauty which has various benefits
for living things, so that when it is focused

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on the ecotourism sector it is hoped that it
will create a conservationist spirit for visitors.
Starting with the understanding that something
found in nature is the best form, followed by
real benefits like ornamental plants, medicinal
plants, and cultural values. Knowledge of the
golden ratio of flowers for visitors is expected
to improve their travel experience and foster a
sense of care for flowers.
IV. CONCLUSION
The golden ratio of flowers is an example
of an interesting finding to study that is useful
for ecotourism interpretation that each flower
species has certain parts that have aesthetic
value, as shown by 12 types of golden ratio
found in this study. These findings show that
each flower has its own beauty value based
on its shape. The shape of flowers can be
assessed objectively by finding the golden ratio
in flowers. It is hoped that these findings can
foster the aesthetic spirit of visitors and a sense
of care for flowers as objects that have beauty
value. This material is very suitable to be used
as part of an ecotourism interpretation because
the aspect of aesthetics is one of the important
aspects needed in implementing ecotourism in
Indonesia.
ACKNOWLEDGMENTS
The authors are grateful to the PPID
Center for Testing Standards for Instruments
for Spices, Medicinal and Aromatic Plants
(Balittro) and PPID for Testing Standards for
Instruments for Ornamental Plants (Balithi)
for their willingness to allow their flowers to be
samples in this study.
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